502 



Propositions containing some Properties of TANGENTS to Circles ; and 

 of TRAPEZIUMS inscribed in Circles, and non-inscribed. Together 

 with Propositions on the Elliptic Representations of CIRCLES, upon 

 a plane Surface, by PERSPECTIVE. By Richard Hey, LL.D. ; late 

 Fellow of Sidney Sussex and Magdalen Colleges, in the University of 

 Cambridge. Communicated by the Rev. Edward Balme, M.A. F.R.S. 

 Read March 31, 1814. [Phil Trans. 1814,^. 348.] 



That the perspective representation of an entire circle is an ellipse, 

 is simply a part of the doctrine of conic sections, and is not in need 

 of demonstration. The principal inquiry of the author has been with 

 regard to the positions of the axes of such ellipses. 



Selecting the case of any number of circles in the same plane, and 

 having their centres in the same line, he examines what law is to be 

 observed in the directions of the axes of the representing ellipses. 



It is shown first, that, excepting one particular case, their axes do 

 not converge to one point, but are parallel to other lines that do con- 

 verge to one point. He does not, however, pretend to determine 

 accurately and separately each of these other lines, but endeavours 

 to ascertain certain limits within which they must be arranged, and 

 a certain regularity in the variation of their directions, which he con- 

 siders sufficient for all the practical purposes of the artist. 



Preparatory to this inquiry are a series of propositions purely geo- 

 metrical, relating to the properties of tangents to circles, and of tra- 

 peziums inscribed in circles, some of which may not be altogether 

 new, but are inserted as necessary to the demonstration of other pro- 

 perties, which he believes have not before been noticed. These are 

 kept separate from the perspective propositions, because they may be 

 more interesting to mathematical readers than they might be if inter- 

 woven with considerations of their application to perspective repre- 

 sentation. The greatest part of this paper of course could not admit 

 of being publicly read, being unintelligible without reference to the 

 figures which accompany it. 



On new Properties of Light exhibited in the optical Phenomena of 

 Mother-of -Pearl, and other Bodies to which the superficial structure 

 of that Substance can be communicated. By David Brewster, LL.D. 

 F.R.S. Edin. and F.S.A. Ed. In a Letter addressed to the Right 

 Hon. Sir Joseph Banks, Bart. K.B. P.R.S. Read April 28, 1 814. 

 [Phil Trans. 1814, /. 397.] 



The first section of this paper is devoted to the optical properties 

 peculiar to mother-of-pearl ; the second to the communication of these 

 properties to other bodies ; the third to the consideration of the cause 

 of these phenomena ; and the fourth to the description of the pecu- 

 liar species of polarization produced by this substance. 



Dr. Brewster observes, mother-of-pearl is composed of laminae, 

 much resembling in their arrangement those of the agate ; that when 

 it is imperfectly polished, a coloured image of a candle is seen in it 



